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Popular Calculus Problems

(\partial)/(\partial x)((x^2-y^2)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}-y^{2}}{x^{2}+y^{2}})
integral of x^{4n}	\int\:x^{4n}dx
tangent of f(x)=(2x-1)/(x+1),\at x=1	tangent\:f(x)=\frac{2x-1}{x+1},\at\:x=1
taylor 3x-cos(x)	taylor\:3x-\cos(x)
derivative of (6x+x^2/((3+x)^2))	\frac{d}{dx}(\frac{6x+x^{2}}{(3+x)^{2}})
limit as n approaches infinity of 0.5^n	\lim\:_{n\to\:\infty\:}(0.5^{n})
derivative of 6sqrt(xe^x)	derivative\:6\sqrt{xe^{x}}
inverse oflaplace ((3s+2))/((s^2+4s+20))	inverselaplace\:\frac{(3s+2)}{(s^{2}+4s+20)}
limit as x approaches 0+of x/(1+ln(x))	\lim\:_{x\to\:0+}(\frac{x}{1+\ln(x)})
y^{''}+7y^'=0,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}+7y^{\prime\:}=0,y(0)=1,y^{\prime\:}(0)=1
(dy)/(dx)=2yx+yx^2,y(-3)=1	\frac{dy}{dx}=2yx+yx^{2},y(-3)=1
tangent of h(x)= 1/(2sqrt(x)),\at x=4	tangent\:h(x)=\frac{1}{2\sqrt{x}},\at\:x=4
limit as x approaches-2 of 2x^2	\lim\:_{x\to\:-2}(2x^{2})
integral of x^3sqrt(5+x^2)	\int\:x^{3}\sqrt{5+x^{2}}dx
derivative of sqrt(x+7)	derivative\:\sqrt{x+7}
integral from 0 to 4 of sqrt(1+36x)	\int\:_{0}^{4}\sqrt{1+36x}dx
integral from 0 to pi of sin(x)cos(2x)	\int\:_{0}^{π}\sin(x)\cos(2x)dx
integral from-1 to 2 of (2-x^2+x)	\int\:_{-1}^{2}(2-x^{2}+x)dx
limit as x approaches 0 of xcos((11)/x)	\lim\:_{x\to\:0}(x\cos(\frac{11}{x}))
derivative of f(x)=-8/(x^3)	derivative\:f(x)=-\frac{8}{x^{3}}
(dy)/(dx)=sqrt(x)y	\frac{dy}{dx}=\sqrt{x}y
limit as t approaches 0 of e^{-5t}	\lim\:_{t\to\:0}(e^{-5t})
derivative of f(x)= 4/3 pix^2	derivative\:f(x)=\frac{4}{3}πx^{2}
(\partial)/(\partial y)((x-y)^2y)	\frac{\partial\:}{\partial\:y}((x-y)^{2}y)
(\partial)/(\partial x)(3arctan(x/y))	\frac{\partial\:}{\partial\:x}(3\arctan(\frac{x}{y}))
derivative of x^x-100	\frac{d}{dx}(x^{x}-100)
y^{''}-8y^'+15y=-sin(2t)	y^{\prime\:\prime\:}-8y^{\prime\:}+15y=-\sin(2t)
y^{''}-2y^'+26y=e^xsin(x)	y^{\prime\:\prime\:}-2y^{\prime\:}+26y=e^{x}\sin(x)
limit as x approaches 0 of 5x^2-4	\lim\:_{x\to\:0}(5x^{2}-4)
(\partial)/(\partial x)(e^{2x+8y})	\frac{\partial\:}{\partial\:x}(e^{2x+8y})
tangent of 8sqrt(x)	tangent\:8\sqrt{x}
inverse oflaplace (ms)/(s^2+s/(nm))	inverselaplace\:\frac{m\cdot\:s}{s^{2}+\frac{s}{n\cdot\:m}}
(\partial)/(\partial x)(y^2(2xe^{2xy}+e^{2xy}*2yx^2))	\frac{\partial\:}{\partial\:x}(y^{2}(2xe^{2xy}+e^{2xy}\cdot\:2yx^{2}))
(\partial)/(\partial x)(2y^3)	\frac{\partial\:}{\partial\:x}(2y^{3})
limit as x approaches 0 of 4/(x(x+2))	\lim\:_{x\to\:0}(\frac{4}{x(x+2)})
derivative of (5x-3)^4(2x-7)^{-3}	derivative\:(5x-3)^{4}(2x-7)^{-3}
limit as x approaches 0+of 8/x-8/(\|x\|)	\lim\:_{x\to\:0+}(\frac{8}{x}-\frac{8}{\left\|x\right\|})
derivative of (3x^2/(sqrt(x)))	\frac{d}{dx}(\frac{3x^{2}}{\sqrt{x}})
derivative of-0.4x^3	\frac{d}{dx}(-0.4x^{3})
limit as x approaches 0 of 5/4 pi-pi	\lim\:_{x\to\:0}(\frac{5}{4}π-π)
limit as x approaches 0 of 1/(2-e^{1/x)}	\lim\:_{x\to\:0}(\frac{1}{2-e^{\frac{1}{x}}})
ty^'+y=t^3,y(1)=-2	ty^{\prime\:}+y=t^{3},y(1)=-2
integral from 1/2 to 1 of (x^{-3}-3)	\int\:_{\frac{1}{2}}^{1}(x^{-3}-3)dx
limit as x approaches 2 of x^3+2x^2+1	\lim\:_{x\to\:2}(x^{3}+2x^{2}+1)
implicit (dy)/(dx),x^3-3xy^2+y^3=1	implicit\:\frac{dy}{dx},x^{3}-3xy^{2}+y^{3}=1
y^'=3x+y,y(0)=5	y^{\prime\:}=3x+y,y(0)=5
integral from 0 to 1 of x/(x^2+4x+13)	\int\:_{0}^{1}\frac{x}{x^{2}+4x+13}dx
tangent of y=2sqrt(x),(1,2)	tangent\:y=2\sqrt{x},(1,2)
derivative of y=(x^4)/(16)	derivative\:y=\frac{x^{4}}{16}
integral of x(3x-5)^{10}	\int\:x(3x-5)^{10}dx
integral of 1/((x)ln(x))	\int\:\frac{1}{(x)\ln(x)}dx
integral of 8/(1+9r^2)	\int\:\frac{8}{1+9r^{2}}dr
derivative of ((x^2)/(x^2+4))	\frac{d}{dx}(\frac{(x^{2})}{x^{2}+4})
f(θ)=sec^2(θ)	f(θ)=\sec^{2}(θ)
(\partial)/(\partial y)(4xy+4y)	\frac{\partial\:}{\partial\:y}(4xy+4y)
sum from n=0 to infinity of-6(1/4)^{2n}	\sum\:_{n=0}^{\infty\:}-6(\frac{1}{4})^{2n}
integral from 0 to 1 of (2x)/((x^2+3)^3)	\int\:_{0}^{1}\frac{2x}{(x^{2}+3)^{3}}dx
limit as x approaches infinity of ((e^{x^4-x^2}))/2	\lim\:_{x\to\:\infty\:}(\frac{(e^{x^{4}-x^{2}})}{2})
derivative of f(x)=xsqrt(1+x^2)	derivative\:f(x)=x\sqrt{1+x^{2}}
y^'+2/t y=0	y^{\prime\:}+\frac{2}{t}y=0
integral of (e^{-2x})/(1+e^{-x)}	\int\:\frac{e^{-2x}}{1+e^{-x}}dx
(\partial)/(\partial x)(3x^2-2xy+x-3y)	\frac{\partial\:}{\partial\:x}(3x^{2}-2xy+x-3y)
sum from n=0 to infinity of 1/(n^2+3)	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{2}+3}
limit as x approaches 1 of-x^2	\lim\:_{x\to\:1}(-x^{2})
integral of 8sin^4(x)cos(x)	\int\:8\sin^{4}(x)\cos(x)dx
derivative of 2/(2-x)	\frac{d}{dx}(\frac{2}{2-x})
integral of ((x^2))/(x^2+1)	\int\:\frac{(x^{2})}{x^{2}+1}dx
(y^4x)(dy)/(dx)=1+x,y(1)=2	(y^{4}x)\frac{dy}{dx}=1+x,y(1)=2
derivative of 5-2(x-2^2)	\frac{d}{dx}(5-2(x-2)^{2})
d/(dy)(sqrt(36-y^2))	\frac{d}{dy}(\sqrt{36-y^{2}})
(\partial)/(\partial x)(7ye^{8x})	\frac{\partial\:}{\partial\:x}(7ye^{8x})
limit as x approaches 0 of 3/(e^x-1)-1/3	\lim\:_{x\to\:0}(\frac{3}{e^{x}-1}-\frac{1}{3})
integral of-4cos(2t+pi)	\int\:-4\cos(2t+π)dt
integral of (4400x)/(4x^2+320)	\int\:\frac{4400x}{4x^{2}+320}dx
(\partial)/(\partial x)(8y^9x^7-7y^8x^6)	\frac{\partial\:}{\partial\:x}(8y^{9}x^{7}-7y^{8}x^{6})
y^'+3x^2y=sin(x)e^{-x^3}	y^{\prime\:}+3x^{2}y=\sin(x)e^{-x^{3}}
limit as x approaches 3 of (8x+7)/(5x+7)	\lim\:_{x\to\:3}(\frac{8x+7}{5x+7})
derivative of 1/4 x^4+1/(8x^2)	\frac{d}{dx}(\frac{1}{4}x^{4}+\frac{1}{8x^{2}})
derivative of 3/(x+6)	\frac{d}{dx}(\frac{3}{x+6})
integral of e^xx-e^x+C	\int\:e^{x}x-e^{x}+Cdx
d/(dy)(yx)	\frac{d}{dy}(yx)
area x,x^{1/2},0,2	area\:x,x^{\frac{1}{2}},0,2
integral of (sec(2x)tan(2x)-4/(x^2))	\int\:(\sec(2x)\tan(2x)-\frac{4}{x^{2}})dx
integral of (x-2)/((x-3)(x-4))	\int\:\frac{x-2}{(x-3)(x-4)}dx
integral of 1/(t^3)	\int\:\frac{1}{t^{3}}dt
limit as x approaches 1+of (1+x)/(x-1)	\lim\:_{x\to\:1+}(\frac{1+x}{x-1})
limit as x approaches-infinity of 5x-2^x	\lim\:_{x\to\:-\infty\:}(5x-2^{x})
(\partial)/(\partial x)((9y)/(x^5))	\frac{\partial\:}{\partial\:x}(\frac{9y}{x^{5}})
f(x)=sqrt(1-4x)	f(x)=\sqrt{1-4x}
(t^2-1)y^'+2ty=0	(t^{2}-1)y^{\prime\:}+2ty=0
derivative of ln((x^3(2x+1))/(x^2-3))	derivative\:\ln(\frac{x^{3}(2x+1)}{x^{2}-3})
(\partial)/(\partial t)(cos(t)-sin(t))	\frac{\partial\:}{\partial\:t}(\cos(t)-\sin(t))
derivative of ((x^2+1^2)/(4x))	\frac{d}{dx}(\frac{(x^{2}+1)^{2}}{4x})
(\partial)/(\partial x)((x+y)/(1+x^2))	\frac{\partial\:}{\partial\:x}(\frac{x+y}{1+x^{2}})
integral of (e^{4x})/(1+e^{4x)}	\int\:\frac{e^{4x}}{1+e^{4x}}dx
y^{''}-4y^'+3y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}-4y^{\prime\:}+3y=0,y(0)=1,y^{\prime\:}(0)=0
(d^4)/(dx^4)(1/(1-x))	\frac{d^{4}}{dx^{4}}(\frac{1}{1-x})
(\partial)/(\partial x)(sin(pi(6x-6y)))	\frac{\partial\:}{\partial\:x}(\sin(π(6x-6y)))
d/(dt)(t+3)	\frac{d}{dt}(t+3)
derivative of (sin(2x)/(cos(3x)))	\frac{d}{dx}(\frac{\sin(2x)}{\cos(3x)})

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